Chapter 8 – PROBABILITY Matt C / 7B


Summary

My task is to prepare for the year 7 exams by presenting the topic, Probability in chapter 8 of our text book.

8.1 Describing Probability

Probability is about how much chance something is to happen. We use words to describe how likely something is to happen.
The words on the scale below are arranged in order from impossible on the bottom to certain at the top.

probability_chart.png


Example 1:
What is the likelihood of the following?

A. tossing a coin and it falls on Heads. .......Answer: Even chance

B. Rolling a dice and it falls on a six. ...........Answer: Very unlikely

C. that the sun will rise tomorrow. ................Answer: Certain

Example 2:

For the spinner, what is Probabiltity of landing on the blue section?
spinner_1_6.png
Answer: very unlikely

8.2 Experimental probability

The experimental probability of an event occurring is the proportion of times that it occurs in the long run. The experimental probability can be found by using the formular probability = the number of times the event occurs ÷ the total number of trials.

Probability_=_number_of_events_%_total_trials.png

Example 1

If a coin is tossed 20 times and 10 Heads occur what is the experimental probability?

Answer: 10 ÷ 20 = 0.5

Example 2

A six sided dice is rolled 300 times and the number 3 occurs 54 times. What is the experimental probability of the number 3 to be rolled?

a_300.png

Answer: 54 ÷ 300 = 0.18


8.3 Experiments in probability


Experiments in probability is carrying out an experimental probability test and recording of data in table from. Each table may be different.

Example 1

In a experiment you will toss a coin 200 times recording how many times it lands on heads. You will need to stop after every ten tosses to update the table.

Number of tosses

Number of heads

Proportion of heads

10


20


30


Record your results in column two.

Use the formular shown earlier to complete column three.


Example 2

In an experiment you roll a dice 10 times to find out the probability of each number is to be rolled.

Outcome

Tally

Frequency

1


2


3


4


5


6


In the tally column you put the amount of those numbers rolled each time and in the frequency column put the experimental probability.

8.4Theoretical probability

The theoretical probability can only be calculated if the outcomes are equaly likely to happen. It can be found by dviding the number of the outcome or outcomes that you want to find by the number of possible outcomes

theoretic_pobability.png

Example 1

A spinner with 5 different colours is spun.

5_colour_spinner.png

A. What is the theoretical probability of green? .........................Answer: 1/5

B. What is the theoretical probability of red, blue or yellow? .....Answer: 3/5

Review

1 Describe the probability of the following with the terms, certain, very likely, likely, even chance, unlikely, very unlikely and impossible. when a dice rolled,

a A number less than five is rolled

b An odd number is rolled

c A number under seven will be rolled

2 Determine the probability of picking a blue lollie out of a packet of red lollies

3 If you throw a basketball 50 times and it goes in 42 times. What is the experimental probability of getting it in?

4 If you flip a coin 24 times and tails comes up 6 times. What is the experimental probability of tails occuring.

5 A spinner with eight sections with different colours is spun 30 times. complete the table below by calculating the frequency.

outcome
tally
frequency
blue
5

yellow
4

green
4

red
2

orange
6

white
4

black
1

purple
4

6 In a experiment you tossed a coin 50 times recording how many times it lands on tails. find out how it's proportion.

Number of tosses

Number of tails

Proportion of tails

10
4

20
11

30
15

40
23

50
29

7 In a car park there are three blue cars, three red cars and four white cars. What is the theoretical probability of a red car to be chosen at random?

8 There are 100 tickets in a raffle if you have 8 tickets what is the theoretical probability of you winning?


Answers

1a verylikely b even chance c certain

2 Impossible 3 0.84

4 0.25

5

outcome
tally
frequency
blue
5
0.1667
yellow
4
0.1334
green
4
0.1334
red
2
0.0667
orange
6
0.2
white
4
0.1334
black
1
0.0334
purple
4
0.1334

6

Number of tosses

Number of tails

Proportion of tails

10
4
0.4
20
11
0.55
30
15
0.5
40
23
0.575
50
29
0.58

7 0.3

8 0.08